The Observed Growth of Massive Galaxy Clusters IV: Robust Constraints on Neutrino Properties

TL;DR

This paper leverages a robust, low-redshift measurement of the matter-power amplitude from a large X-ray cluster sample to constrain neutrino properties. By combining the cluster X-ray luminosity function with CMB, gas-mass fraction, SNIa, BAO, and conservative systematics within a Markov Chain Monte Carlo framework, it tightens bounds on the species-summed neutrino mass $M_\nu$ and the effective number of relativistic species $N_{\mathrm{eff}}$, while assessing the impact of extending the cosmological model to include curvature and tensor modes. In a simple flat $\Lambda$CDM+$M_\nu$ scenario, the inclusion of XLF data yields $M_\nu<0.33$ eV (95.4% CL), demonstrating the power of cluster-based $\sigma_8$ constraints to break degeneracies with neutrino mass. In more general models, the limits weaken but remain informative (e.g., $M_\nu<0.70$ eV with $H_0$ prior; $N_{\mathrm{eff}}=3.7\pm0.7$). The results align with other recent analyses and underscore the value of combining low- and high-redshift structure measurements; future Planck data and improved $H_0$ and $\sigma_8$ constraints could push these limits further and potentially reveal hints of nonzero neutrino mass or additional relativistic species.

Abstract

This is the fourth of a series of papers in which we derive simultaneous constraints on cosmological parameters and X-ray scaling relations using observations of the growth of massive, X-ray flux-selected galaxy clusters. Here we examine the constraints on neutrino properties that are enabled by the precise and robust constraint on the amplitude of the matter power spectrum at low redshift that is available from our data. In combination with cluster gas-mass fraction, cosmic microwave background, supernova and baryon acoustic oscillation data, and incorporating conservative allowances for systematic uncertainties, we limit the species-summed neutrino mass, M_nu, to <0.33 eV at 95.4 per cent confidence in a spatially flat, cosmological constant (LambdaCDM) model. In a flat LambdaCDM model where the effective number of neutrino species, N_eff, is allowed to vary, we find N_eff = 3.4 -0.5 +0.6 (68.3 per cent confidence, incorporating a direct constraint on the Hubble parameter from Cepheid and supernova data). We also obtain results with additional degrees of freedom in the cosmological model, in the form of global spatial curvature (Omega_k) and a primordial spectrum of tensor perturbations (r and n_t). The results are not immune to these generalizations; however, in the most general case we consider, in which M_nu, N_eff, curvature and tensors are all free, we still obtain M_nu < 0.70 eV and N_eff = 3.7 +- 0.7 (at respectively the same confidence levels as above). These results agree well with recent work using independent data, and highlight the importance of measuring cosmic structure and expansion at low as well as high redshifts. Although our cluster data extend to redshift z=0.5, the effect of neutrino mass on the growth of structure at late times is not yet detected at a significant level.

Figures (6)

• Figure 1: Joint 68.3 and 95.4 per cent confidence regions in the $M_\nu$-$\sigma_8$ plane from the combination of CMB, $f_{\mathrm{gas}}$, SNIa and BAO data (blue), and the combination of those data with the XLF (gold). The XLF data provide a tight constraint on $\sigma_8$, breaking the degeneracy in this plane. To demonstrate the robustness of constraints on $M_\nu$ obtained using the XLF data, we compare (left panel) results for a simple $\Lambda$CDM+$M_\nu$ model with (right panel) results obtained when nuisance parameters are included in the model (in this case, $\Omega_{\mathrm{k}}$, $r$ and $n_{\mathrm{t}}$; note the difference in scale). Note that conservative systematic uncertainties are included here (and in all subsequent figures).
• Figure 2: [ preprint note: a monochrome version of this figure appears after the references, as Figure \ref{['fig:msdegenbw']}] Joint 95.4 per cent confidence regions for $M_\nu$ and $\sigma_8$ for various cosmological models. Yellow contours correspond to the basic $\Lambda$CDM+$M_\nu$ model, blue contours are marginalized over $\Omega_{\mathrm{k}}$, red contours over $w$, green over $r$ and $n_{\mathrm{t}}$, and purple over $N_{\mathrm{eff}}$. The left panel shows constraints obtained from the combination of CMB, $f_{\mathrm{gas}}$, SNIa and BAO data; the right panel shows results that include the XLF in addition to those data. No external prior on $H_0$ is used.
• Figure 3: Joint 68.3 and 95.4 per cent confidence regions on $\Omega_{\mathrm{m}} h^2$ and $N_{\mathrm{eff}}$ from the combination of CMB, $f_{\mathrm{gas}}$, SNIa and BAO data with a direct measurement of $H_0$ (blue), and the same data with the addition of the XLF (gold). Also shown are the constraints from the former combination of data, but without the prior on $H_0$ (green); this illustrates the strong sensitivity of the $N_{\mathrm{eff}}$ results to the Hubble parameter. The dotted, horizontal line indicates the standard value of $N_{\mathrm{eff}}$, 3.046.
• Figure 4: Joint constraints on $\Omega_{\mathrm{b}}/\Omega_{\mathrm{m}}$ and $H_0$ when $N_{\mathrm{eff}}$ is free. Green contours show results obtained from the combination of CMB, $f_{\mathrm{gas}}$, SNIa and BAO data; despite the inclusion of SNIa and BAO data, the strong degeneracy in this plane that occurs in both $f_{\mathrm{gas}}$ and CMB analyses (when $N_{\mathrm{eff}}$ is free) remains evident. The addition of a measurement of the Hubble parameter at the 5 per cent level (blue contours) significantly improves the results.
• Figure 5: Joint 68.3 and 95.4 per cent confidence regions on $\Omega_{\mathrm{m}} h^2$ and $\sigma_8$ from the combination of CMB, $f_{\mathrm{gas}}$, SNIa and BAO data with a direct measurement of $H_0$ (blue), and the same data with the addition of the XLF (gold) when $N_{\mathrm{eff}}$ is free. The tight constraint on $\sigma_8$ provided by the XLF data improves the determination of $\Omega_{\mathrm{m}} h^2$, which translates to an improved constraint on $N_{\mathrm{eff}}$ (Figure \ref{['fig:hnlcdm']}).